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Surfer Ben Gerring has died in a Perth hospital four days after being attacked by a great white shark at Falcon, south of Mandurah.

The 29-year-old lost his leg above the knee in a savage attack about 250m from shore at Surf Break Lookout on Tuesday afternoon. He was flown to Royal Perth Hospital but sadly succumbed to his injuries.

Mr Gerring's fiancee, Jasmine Boyer, was pregnant with the couple's child. She kept a bedside vigil before Mr Gerring's condition worsened on Friday.

Scientists earlier confirmed the shark that the shark responsible for the attack was a great white. They examined bite marks on pieces of surfboard recovered from the sea. They could not, however, determine the size of the shark.

Mandurah beaches have reopened, as has the debate about culling the large ocean predators.

On Wednesday morning, Fisheries WA officers set baited drum lines in the bay and hooked a 4.2m great white, which died on the hook and was then towed out to sea and disposed of, after officers took measurements and samples.

The Humane Society questioned whether the shark caught and killed on Wednesday was responsible for Tuesday's attack.

A fundraising page set up to help Mr Gerring and his fiancee has received more than $24,000 in donations.

"The family would like to thank everyone for there ongoing support, your messages are keeping the family spirits high," the page reads.

Mr Gerring was raised south of Perth and was known locally among surfers, including Mandurah Boardriders Club president Brian Williams, who was among the first on scene.